How can I clone a polygon based on multiple spatial (point) intersects?

I have a case where a polygon is overlapped by several points stacked on top of a polygon (kind of like coins stacked on top of a coaster).

I would like to clone the polygon so that the attributes of each point are merged to the corresponding overlapping polygon. In the end I have 1 polygon for each point, e.g.,

Before:

1 coaster, three overlapping coins:

After:

3 coasters, one for each overlapping coin.

Thanks,

Pete